Stable rational modification of a weight (Q1969410)

Let \(\mu\) denote a nonnegative measure with support \(\text{supp}(\mu)\) in \(\mathbb{R}\) such that the moments \(\mu_n= \int t^n d\mu(t)\), \(n= 0,1,\dots\), all exist. Let \(\widetilde\mu\) denote the modified weight \[ d\widetilde\mu(t)= {d\mu(t)\over \omega(t)}, \] where \(\omega(t)\) is polynomial that is positive on the interval \(I\), the convex hull of \(\text{supp}(\mu)\). Let the coefficients of the three-term recurrence equation \[ P_{n+ 1}= (z- a_n) P_n- b_n P_{n-1} \] satisfied by the orthogonal polynomials relative to \(\mu\) be given. A stable algorithm for calculating the coefficients \(\widetilde a_n\), \(\widetilde b_n\) of the recurrence equation satisfied by the orthogonal polynomials relative to \(\widetilde\mu\) is constructed.